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Upper limit on the η → π+π− branching ratio

with the KLOE detector.

The KLOE Collaboration

F. Ambrosino f, A. Antonelli b, M. Antonelli b, C. Bacci k,

M. Barva k, P. Beltrame b, G. Bencivenni b, S. Bertolucci b,C. Bini i, C. Bloise b, V. Bocci i, F. Bossi b, D. Bowring b,m,

P. Branchini k, R. Caloi i, P. Campana b, G. Capon b,

T. Capussela f, G. Carboni j, F. Ceradini k, F. Cervelli g,S. Chi b, G. Chiefari f, P. Ciambrone b, S. Conetti m,

E. De Lucia i, A. De Santis i, P. De Simone b, G. De Zorzi i,S. Dell’Agnello b, A. Denig c, A. Di Domenico i, C. Di Donato f,

S. Di Falco g, B. Di Micco k, A. Doria f, M. Dreucci b,A. Farilla k, G. Felici b, A. Ferrari b, M. L. Ferrer b,

G. Finocchiaro b, C. Forti b, P. Franzini i, C. Gatti i, P. Gauzzi i,S. Giovannella b, E. Gorini d, E. Graziani k, M. Incagli g,W. Kluge c, V. Kulikov e, F. Lacava i, G. Lanfranchi b,

J. Lee-Franzini b,ℓ, D. Leone i, M. Martemianov b, M. Martini b,P. Massarotti f, M. Matsyuk b, W. Mei b, S. Meola f, R. Messi j,

S. Miscetti b, M. Moulson b, S. Muller c, F. Murtas b,M. Napolitano f, F. Nguyen k, M. Palutan b, E. Pasqualucci i,

L. Passalacqua b, A. Passeri k, V. Patera b,h, F. Perfetto f,L. Pontecorvo i, M. Primavera d, P. Santangelo b, E. Santovetti j,

G. Saracino f, B. Sciascia b, A. Sciubba b,h, F. Scuri g,

I. Sfiligoi b, T. Spadaro b, E. Spiriti k, M. Testa i, L. Tortora k,P. Valente b, B. Valeriani c, G. Venanzoni b, S. Veneziano i,

A. Ventura d, S. Ventura i, R. Versaci k, I. Villella f, G. Xu a,b,

aInstitute of High Energy Physics of Academica Sinica, Beijing, China.

bLaboratori Nazionali di Frascati dell’INFN, Frascati, Italy.

cInstitut fur Experimentelle Kernphysik, Universitat Karlsruhe, Germany.

dDipartimento di Fisica dell’Universita e Sezione INFN, Lecce, Italy.

eInstitute for Theoretical and Experimental Physics, Moscow, Russia.

Preprint submitted to Elsevier Science 20 May 2011

fDipartimento di Scienze Fisiche dell’Universita “Federico II” e Sezione INFN,

Napoli, Italy

gDipartimento di Fisica dell’Universita e Sezione INFN, Pisa, Italy.

hDipartimento di Energetica dell’Universita “La Sapienza”, Roma, Italy.

iDipartimento di Fisica dell’Universita “La Sapienza” e Sezione INFN, Roma,

Italy.

jDipartimento di Fisica dell’Universita “Tor Vergata” e Sezione INFN, Roma,

Italy.

kDipartimento di Fisica dell’Universita “Roma Tre” e Sezione INFN, Roma, Italy.

ℓPhysics Department, State University of New York at Stony Brook, USA.

mPhysics Department, University of Virginia, USA.

Corresponding author: Cesare Bini, e-mail cesare.bini@roma1.infn.it, tel

+390649914266, fax +39064957697

Abstract

We have searched with the KLOE detector for the P and CP violating decay η →π+π− in a sample of 1.55 × 107 η’s from the decay φ → ηγ of φ-mesons producedin e+e− annihilations at DAΦNE. No signal is found. We obtain the upper limitBR(η → π+π−)< 1.3×10−5 at 90% confidence level.

Key words: Decays of η mesons, discrete symmetriesPACS: 11.30.Er, 13.25.Jk, 14.40.Aq

The study of η decays provides an excellent laboratory for testing the validityof symmetries of the physical world. The decay η → π+π− violates both P andCP invariance. In the Standard Model, the reaction can proceed only via theweak interaction with a branching ratio of order 10−27 according to Ref.[1].Higher branching ratios are conceivable either introducing a CP violation termin the QCD lagrangian through the so-called θ term (a branching ratio up to10−17 can be obtained in this scheme compatible with the experimental limiton the neutron electric dipole momentum) or allowing a CP violation in theextended Higgs sector (in this case 10−15 can be reached) as described inRef.[1]. The detection of this decay at any level accessible today would signalP and CP violation from new sources, beyond any considerable extension ofthe Standard Model. The best published previous result from a direct searchfor the η decay to π+π− was obtained in 1999: BR(η → π+π−) < 3.3 × 10−4

at 90% confidence level [2].

We present here the result of a direct search for this decay performed with the

2

KLOE experiment at the Frascati φ factory, DAΦNE, based on an integratedluminosity of 350 pb−1 collected in the years 2001 and 2002. DAΦNE is an e+e−

collider working at the centre of mass energy of 1019.5 MeV, i.e., at the φmass.φ mesons are produced nearly at rest in the laboratory. Beams in DAΦNEcollide with a crossing angle of π−0.025 rad. φ-mesons are therefore producedwith a momentum | ~pφ| ∼ 12.5 MeV/c in the horizontal plane, directed towardsthe centre of the storage rings. The precise value of the φ momentum, togetherwith the centre of mass energy and the beam spot position, is determined runby run using Bhabha scattering events.

The total cross section for e+e−→φ is ∼3 µb. η mesons are copiously producedat a typical rate of ∼2 Hz through the radiative decay φ → ηγ, which has abranching ratio of 1.3%. In the decay chain φ → ηγ → π+π−γ, the photonis monochromatic (Eγ = 363 MeV) and is emitted according to an angulardistribution dN/d cos θγ ∼ (1 + cos2 θγ), where θγ is the polar angle of theemitted photon with respect to the beam line. The invariant mass of theπ+π− pair is equal to the η mass: Mππ=Mη=547.3 MeV.

The KLOE detector consists of a large-volume drift chamber [3] (3.3 m lengthand 2 m radius), operated with a 90% helium-10% isobutane gas mixture, anda sampling calorimeter [4] made of lead and scintillating fibres. The calorimeterconsists of a cylindrical barrel and two endcaps providing a solid angle coverageof 98%. A superconducting coil surrounds the entire detector and produces asolenoidal field B=0.52 T.

Tracks are reconstructed in the drift chamber with a momentum resolution ofσ(p⊥)/p⊥ < 0.4%. Clusters of energy deposits in the calorimeter are classifiedeither as associated to charged tracks (charged pions, electrons or muons) oras isolated (photons, KL). Photon energies and arrival times are measured

with resolutions of σE/E = 5.7%/√

E(GeV) and σt = 54ps/√

E(GeV) ⊕ 50ps; impact positions are measured with a resolution of a few centimetres. Thereadout granularity is 4.5 × 4.5 cm2 in the plane transverse to the fibres,and is segmented in five layers along the particles direction. The trigger [5]is based on the detection of at least two energy deposits in the calorimeterabove a threshold that ranges between 50 MeV in the barrel and 150 MeV inthe endcaps. The higher machine background rates at small angle requires ahigher threshold in the endcaps.

Samples of simulated events are obtained using the GEANFI [6] code basedon GEANT: event generators for any specific final state, including decay dy-namics and radiative corrections, are provided together with the detailed de-scription of the geometry and the response of each sub-detector.

The decay chain φ→ ηγ → π+π−γ is searched for by selecting events with twotracks of opposite charge with a vertex near the e+e− interaction point and

3

one prompt photon matching the missing energy and momentum obtainedfrom the π+π− pair and the φ kinematic variables. The vertex is requiredto be inside a cylinder 20 cm long and 8 cm in radius, with axis parallel tothe beam line, centred at the beam spot position. The polar angle θt of eachtrack is required to satisfy 45◦< θt <135◦. A prompt photon is detected asan energy cluster not associated to any track, with time of flight Tcl, distancefrom the beam spot position Rcl, and energy Ecl satisfying the condition |Tcl−Rcl/c| < 5σt(Ecl), where σt is the energy-dependent time resolution. In orderto match the missing energy and momentum obtained from the π+π− pairwith the photon kinematics, the angle ψ between the direction of the missingmomentum and the direction of the photon is required to be less than 0.15rad.

Each track is extrapolated to the calorimeter and is required to be associatedwith a calorimeter cluster. A major source of background is due to radia-tive Bhabha events, e+e−→e+e−γ. Rejection of these events is based on theshower energy deposition in the calorimeter, on the time of flight, which isdifferent for electrons and pions, and on kinematics. A likelihood estimator isconstructed using the following information: the total energy of the cluster andthe maximum energy release among the five planes of the calorimeter; the en-ergy release in the first and in the last fired calorimeter plane; and |Tcl −L/c|,where L is the track length from the interaction point to the centroid of thecluster. The probability density function for each variable is obtained usingsamples of unambiguously identified pions from π+π−π0 and π+π− events.The separation between π+π−γ and e+e−γ events based on the values of thelikelihood estimators L+ and L− for positive and negative particles is shownin Fig. 1.

µ+µ−γ and residual e+e−γ events are rejected using the so called track-mass

variable MT . MT is the particle mass computed assuming the φ decays to twoparticles of identical mass plus a photon. MT is given by:

|~pφ − ~p1 − ~p2| = Eφ −√

p21 +M2

T −√

p22 +M2

T (1)

where ~p1 and ~p2 are the three-momenta of the two pions and Eφ and ~pφ are thetotal centre-of-mass energy and momentum respectively. The track mass valueis obtained from tracking information only and is very weakly correlated tothe likelihood estimator value. The requirement 129 < MT < 149 MeV selectsπ+π−γ events; see Fig. 2. This cut, together with the cut on ψ described above,ensures that background due to φ→ π+π−π0 events is negligible.

The Mππ spectrum of the selected events ranges from 2mπ=279 MeV toMφ=1019.5 MeV. Apart from the hypothetical signal, the physical processeswhich give π+π−γ final states are e+e− → π+π− accompanied by ISR (initialstate radiation) or FSR (final state radiation), φ→ f0(980)γ with f0(980) →

4

-6

-4

-2

0

2

4

6

8

10

-6 -4 -2 0 2 4 6 8 10

L-

L+

Fig. 1. Scatter plot of the likelihood variable for positive (L+) and negative (L−)particles in arbitrary units. The line is the cut applied to select pion and muon pairs(above) from electron pairs (below).

M (MeV)

3Counts x 10 / 0.5 MeV

1

3

4

T

2

160140120100

Fig. 2. Distribution of the track mass variable MT showing the separation betweenthe peaks due to π+π−γ events (right peak) and to µ+µ−γ events (left peak).

π+π− and φ→ ρ±π± with ρ± → π±γ. Analyses of the full spectrum in differ-ent photon angular ranges are reported elsewhere [7,8]. Here we are interestedin the Mππ region around the η mass where the signal is expected to be. The ηmass region (500 - 600 MeV) of the Mππ spectrum is dominated by ISR eventswith the radiated photon mostly at small polar angle. To reduce the amountof such events while keeping a reasonable acceptance, we require the photonto be at large angle (45◦ < θγ < 135◦).

From Monte Carlo simulation we find the overall signal efficiency to be,ǫs=(16.6±0.2stat±0.4syst)%. The 2% systematic uncertainty is estimated by

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comparing the data and Monte Carlo distributions of the variables MT andψ. The overall rejection factors for the backgrounds range between order 104

for µ+µ−γ and 106 for π+π−π0 and e+e−γ.

The expected Mππ distribution for a possible signal is a Gaussian with aresolution of 1.33 MeV. Analysis of the similar and abundant decay Ks →π+π− shows that the Monte Carlo correctly reproduces the observed massdistribution (see Ref. [6]). Figure 3 shows the measured Mππ spectrum in the

0

50

100

150

200

250

300

510 520 530 540 550 560 570 580 590

Events / 1.2 MeV

Mππ (MeV)

Fig. 3. π+π− mass spectrum between 500 and 600 MeV superimposed to the fittedbackground. The Gaussian is the expected signal shape in arbitrary units.

region around the η mass, in 1.2 MeV bins, together with the expected formfor the signal. No evidence for the signal is observed. The curve superimposedto the data is the result of a fit to the Mππ spectrum over a much widerinterval, from 410 MeV up to 1010 MeV with a function that describes all theappropriate physical processes:

dN

dMππ

=

(

d σ(ISR)

dMππ

+d σ(FSR+ f0)

dMππ

+d σ(ρπ)

dMππ

)

× L× ǫ(Mππ). (2)

In Eq. 2 above, L is the integrated luminosity of the sample analysed, ǫ(Mππ)is the selection efficiency as a function of Mππ for the full range of the fit, andthe d σ/dMππ terms are the differential cross sections for the various processeswhich contribute to the background. The fit has 7 free paramaters and givesa χ2 value of 75 for 84 data points in the 500 - 600 MeV region and a valueof 539 for 488 data points in the full mass range. 4 out of the 7 parametersdescribe the pion form factor according to Ref.[9]: Mρ, Γρ, α and β; the other3 describe the scalar contribution according to Ref.[10]: Mf0

, gf0KK and gf0ππ.The result of this fit does not change if we remove the data points in the signal

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region. We use this result as the estimate of the background magnitude in thefollowing.

In order to determine an upper limit for the branching ratio, we have repeatedthe fit by adding to the previously estimated background a signal componentrepresented by a Gaussian with fixed mean and width of 547.3 and 1.33 MeVrespectively, and free absolute normalisation. The fit returns a number ofsignal events Ns = −8±24, compatible with zero. The result does not dependon the choice of the fit interval and bin size. The probability distribution of Ns

has been checked by generating a large number of histograms according to thebackground distribution and fitting each of them to get Ns. The results of thissimple simulation show that Ns, in the case of no signal, is indeed Gaussiandistributed with a mean compatible with zero and a width of 24. The 90%confidence-level upper limit on the number of events is obtained using thetables in Ref. [11]. We find Ns < 33.

Alternatively, we have used a polynomial parametrisation of the background,obtained by fitting the sideband regions (500 - 540 MeV and 555 - 600 MeV)only. Applying the same procedure to get Ns, we obtain Ns = −10 ± 24 andconsequently Ns < 31. The systematic uncertainty due to the parametrisationof the background is small and we use the largest value for the limit.

The total number of η’s in the sample, Nη, is evaluated counting the number ofφ→ ηγ events with η → 3π0. The efficiency for this channel is ǫ(φ→ ηγ, η →3π0) = 0.378±0.001stat±0.008syst, where the 2% systematic error is dominatedby the uncertainty on the detection efficiency of low energy photons. Usingthe known branching fraction BR(η → 3π0)=0.3251±0.0029 [12] we obtain:

Nη =N(η → 3π0)

ǫ(φ→ ηγ, η → 3π0) ×BR(η → 3π0)= 1.55 × 107 (3)

with a systematic uncertainty due to the knowledge of the efficiencies and ofthe intermediate branching ratio of 2%.

Taking the result Ns < 33, the 90% confidence-level upper limit is

BR(η → π+π−) =Ns

Nηǫ(η → π+π−)< 1.3 × 10−5. (4)

This result is the best obtained to date and is 25 times more stringent thanthe previous best limit.

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Acknowledgements

We thank the DAFNE team for their efforts in maintaining low backgroundrunning conditions and their collaboration during all data-taking. We wantto thank our technical staff: G.F.Fortugno for his dedicated work to ensurean efficient operation of the KLOE Computing Center; M.Anelli for his con-tinuos support to the gas system and the safety of the detector; A.Balla,M.Gatta, G.Corradi and G.Papalino for the maintenance of the electronics;M.Santoni, G.Paoluzzi and R.Rosellini for the general support to the detec-tor; C.Piscitelli for his help during major maintenance periods. This work wassupported in part by DOE grant DE-FG-02-97ER41027; by EURODAPHNE,contract FMRX-CT98-0169; by the German Federal Ministry of Educationand Research (BMBF) contract 06-KA-957; by Graduiertenkolleg ‘H.E. Phys.and Part. Astrophys.’ of Deutsche Forschungsgemeinschaft, Contract No. GK742; by INTAS, contracts 96-624, 99-37; and by TARI, contract HPRI-CT-1999-00088.

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